Solutions for the questions from Rotational Dynamics (Chapter 1 - Physics Class 12 Maharashtra board)
Q. (i) from Choose the correct option.; Q. (i) and (ii) from Answer in brief; and Q. 12, 13, 14, 15, and 16. All these questions are from Exercises section at the end of the chapter (Page no. 23, 24 and 25)

Questions:

00:01
i) When seen from below, the blades of a ceiling fan are seen to be revolving anticlockwise and their speed is decreasing. Select the correct statement about the directions of its angular velocity and angular acceleration.
(A) Angular velocity upwards, angular acceleration downwards.
(B) Angular velocity downwards, angular acceleration upwards.
(C) Both, angular velocity and angular acceleration, upwards.
(D) Both, angular velocity and angular acceleration, downwards.

02:09
2. Answer in brief
i) Why are curved roads banked?
ii) Do we need a banked road for a two wheeler? Explain.

03:29
12. Somehow, an ant is stuck to the rim of a
bicycle wheel of diameter 1 m. While the
bicycle is on a central stand, the wheel
is set into rotation and it attains the
frequency of 2 rev/s in 10 seconds, with
uniform angular acceleration. Calculate
(i) Number of revolutions completed by
the ant in these 10 seconds. (ii) Time
taken by it for first complete revolution
and the last complete revolution.

10:23
13. Coefficient of static friction between
a coin and a gramophone disc is 0.5.
Radius of the disc is 8 cm. Initially the
centre of the coin is π cm away from
the centre of the disc. At what minimum
frequency will it start slipping from there? By what factor will the answer
change if the coin is almost at the rim?
(use g = π2 m/s2)

16:40
14. Part of a racing track is to be designed
for a curvature of 72 m. We are not
recommending the vehicles to drive
faster than 216 kmph. With what angle
should the road be tilted? By what height
will its outer edge be, with respect to the
inner edge if the track is 10 m wide?

21:15
15. The road in the question 14 above is
constructed as per the requirements. The
coefficient of static friction between the
tyres of a vehicle on this road is 0.8, will
there be any lower speed limit? By how
much can the upper speed limit exceed in
this case?

25:04
16. During a stunt, a cyclist (considered to
be a particle) is undertaking horizontal
circles inside a cylindrical well of
radius 6.05 m. If the necessary friction
coefficient is 0.5, how much minimum
speed should the stunt artist maintain?
Mass of the artist is 50 kg. If she/he
increases the speed by 20%, how much
will the force of friction be?